How about stating the whole question, using the exact wording.
I don't know if this is the correct sub-forum for this question. If it isn't, I'm sorry.
I have this expression that expands based on the variables given:
What I want to do is generalize this expression, i.e.: , but I don't know how to go about this. I think I have to use recursion but I don't see how it should be done.
Any help with this would be appreciated.
It is not a math question from a book or a teacher. It's an expression of how many comparisons an agorithm (made by me and another) makes in a worst case scenario. If my question is in any way not clear I will try to explain it better?
The second variable (y) determines the number of summations, the number of factors the summations operate on, and the number of overall terms.
The y terms each contain y-1 summations, each summation having a lower bound of 0. The upper bound of the summations depends on the term. In the first term all upper bounds are x-1, in the second term one upper bound is x-2 and the others are x-1, in the third term two upper bounds are x-2 and the others are x-1, and so on.
How many factors the summations operate on is equal to y-1, one factor for each summation. Each factor is x-i, where i is one of the summation indices.
I hope that helps to clear it up.